Columbia & NYU Financial Engineering Colloquium: Agostino Capponi, Rama Cont, & Xin Guo

4 pm - 4:50 pm | Agostino Capponi

Professor
Department of Industrial Engineering and Operations Research
Columbia University

Title

Data-Driven Dynamic Factor Modeling via Manifold Learning

Abstract

We propose a data-driven dynamic factor framework where a response variable $y(t) \in \mathbb{R}^m$ depends on a high-dimensional set of covariates $x(t) \in \mathbb{R}^d$ without imposing any parametric model on the joint covariate dynamics. Leveraging diffusion maps - a nonlinear manifold learning technique introduced in Coifman and Lafon [2006] - our framework uncovers the joint dynamics of the covariates in a purely data-driven way. It achieves this by constructing lower-dimensional covariate embeddings that retain most of the explanatory power for the time series of responses $y(t)$, while exhibiting simple linear dynamics. We combine diffusion maps with Kalman filtering techniques to infer the latent dynamic covariate embeddings, and predict the response variable directly from the diffusion map embedding space.

We apply the framework to stress testing equity portfolios using a combination of financial and macroeconomic factors from the FED's supervisory scenarios. Unlike standard scenario analysis (SSA), where one assumes that the conditional expectation of the unstressed factors given the scenario is zero, we account for dynamic correlation between stressed and unstressed risk factors through a novel conditional sampling procedure. We demonstrate that our data-driven stress testing procedure outperforms SSA- and PCA-based benchmarks through historical backtests spanning three major financial crises, achieving reductions in mean absolute error (MAE) of up to 52\% and 57\% for scenario-based portfolio return prediction, respectively. (joint work with Graeme Baker and Jose Sidaoui Gali).

4:50 pm - 5:40 pm | Xin Guo

Professor, UC Berkeley

Title

An alpha-potential game framework for N-player games

Abstract

Recently we proposed a general framework of dynamic N-player non-cooperative games called α-potential games, where the change of a player's value function upon her unilateral deviation from her strategy is equal to the change of an α-potential function up to an error α. In this talk, we will discuss some of the latest developments in this game framework. First, we report an analytical characterization of α-potential functions, with α represented in terms of the magnitude of the asymmetry of value functions' second-order derivatives. Next, for stochastic differential games in which the state dynamic is a controlled diffusion, we show that α is characterized in terms of the number of players, the choice of admissible strategies, and the intensity of interactions, and the level of heterogeneity among players. Two classes of stochastic differential games, namely distributed games, and games with mean-field interactions, are analyzed to highlight the dependence of α on general game characteristics that are beyond the mean-field paradigm, which focuses on the limit of N with homogeneous players. Finally, we show how to analyze the α-NE in this game through analyzing a conditional McKean-Vlasov control problem.

5:40 pm - 6:30 pm | Rama Cont

Professor, Oxford

Title

Dynamic hedging with misspecified models

Abstract

It is commonly assumed that a detailed and accurate description of the joint dynamics of risk factors and asset prices is a prerequisite for the design of (good) hedging and risk management strategies for derivative portfolios. This has motivated the development of increasingly complex stochastic models with many risk factors and parameters, which are challenging to estimate and implement.

We argue that this assumption is incorrect. We show that any 'auxiliary' pricing model capable of calibrating the cross-section of liquid option prices and satisfying an identifiability assumption is capable of recovering market dynamics through parameter recalibration, and enables to compute adequate hedge ratios without explicit knowledge of market dynamics.

We provide explicit formulas for hedge ratios in dynamically recalibrated models and show that they are different from raw model sensitivities and contain adjustment terms related to parameter recalibration.

We argue that this approach is an effective recipe for dynamic hedging under model uncertainty and pleads in favor of computationally flexible models with good inversion properties.